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Simplifying 15c2 + (348.4) * c + -11912 = 0 Reorder the terms: -11912 + 348.4c + 15c2 = 0 Solving -11912 + 348.4c + 15c2 = 0 Solving for variable 'c'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -794.1333333 + 23.22666667c + c2 = 0 Move the constant term to the right: Add '794.1333333' to each side of the equation. -794.1333333 + 23.22666667c + 794.1333333 + c2 = 0 + 794.1333333 Reorder the terms: -794.1333333 + 794.1333333 + 23.22666667c + c2 = 0 + 794.1333333 Combine like terms: -794.1333333 + 794.1333333 = 0.0000000 0.0000000 + 23.22666667c + c2 = 0 + 794.1333333 23.22666667c + c2 = 0 + 794.1333333 Combine like terms: 0 + 794.1333333 = 794.1333333 23.22666667c + c2 = 794.1333333 The c term is 23.22666667c. Take half its coefficient (11.61333334). Square it (134.8695113) and add it to both sides. Add '134.8695113' to each side of the equation. 23.22666667c + 134.8695113 + c2 = 794.1333333 + 134.8695113 Reorder the terms: 134.8695113 + 23.22666667c + c2 = 794.1333333 + 134.8695113 Combine like terms: 794.1333333 + 134.8695113 = 929.0028446 134.8695113 + 23.22666667c + c2 = 929.0028446 Factor a perfect square on the left side: (c + 11.61333334)(c + 11.61333334) = 929.0028446 Calculate the square root of the right side: 30.479547972 Break this problem into two subproblems by setting (c + 11.61333334) equal to 30.479547972 and -30.479547972.Subproblem 1
c + 11.61333334 = 30.479547972 Simplifying c + 11.61333334 = 30.479547972 Reorder the terms: 11.61333334 + c = 30.479547972 Solving 11.61333334 + c = 30.479547972 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-11.61333334' to each side of the equation. 11.61333334 + -11.61333334 + c = 30.479547972 + -11.61333334 Combine like terms: 11.61333334 + -11.61333334 = 0.00000000 0.00000000 + c = 30.479547972 + -11.61333334 c = 30.479547972 + -11.61333334 Combine like terms: 30.479547972 + -11.61333334 = 18.866214632 c = 18.866214632 Simplifying c = 18.866214632Subproblem 2
c + 11.61333334 = -30.479547972 Simplifying c + 11.61333334 = -30.479547972 Reorder the terms: 11.61333334 + c = -30.479547972 Solving 11.61333334 + c = -30.479547972 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-11.61333334' to each side of the equation. 11.61333334 + -11.61333334 + c = -30.479547972 + -11.61333334 Combine like terms: 11.61333334 + -11.61333334 = 0.00000000 0.00000000 + c = -30.479547972 + -11.61333334 c = -30.479547972 + -11.61333334 Combine like terms: -30.479547972 + -11.61333334 = -42.092881312 c = -42.092881312 Simplifying c = -42.092881312Solution
The solution to the problem is based on the solutions from the subproblems. c = {18.866214632, -42.092881312}
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